Magnetic Resonance Imaging

Question 1

What causes a nucleui to spin?

Answer 1

Spin is a fundamental property of nature like electrical charge or mass, comes in multiples of 1/2 and can be either + or -. Individual unpaired electrons, protons, and neutrons each possesses a spin of 1/2, i.e nucleus with either an odd atomic number or an odd mass number has an angular momentum, or spin angular momentum.

Two or more particles with spins having opposite signs can pair up to eliminate the observable manifestations of spin. An example is helium. In nuclear magnetic resonance, it is unpaired nuclear spins that are of importance.

Question 2

Mention an important effect spin has on for instance protons

Answer 2

A proton has the property called spin. Think of the spin of a proton as a magnetic moment vector, causing the proton to behave like a tiny magnet with a north and south pole.

When the proton is placed in an external magnetic field B₀, the spin vector of the particle aligns itself with the external field, just like a magnet would. There is a low energy configuration or state where the poles are aligned N-S-N-S and a high energy state N-N-S-S.

Question 3

Explain Magnetization

Answer 3

The ¹H nuclei in the human body, when placed in a magnetic field, B₀ , will build up a magnetization M.

At 1T, the excess of magnetic moments of the 1H nuclei aligned with the external magnetic field are 10 ppm. They produces a net magnetization, M.

Question 4

Explain Magnetization Torque

Answer 4

If the Magnetization is brought out of the alignment with B₀, it will experience a torque which acts to return the net Magnetization to alignment

Question 5

Explain Lamor’s equation

Answer 5

When placed in a magnetic field of strength B₀, a particle with a net spin can absorb a photon of frequency f . The frequency f depends on the gyromagnetic ratio y (gamma) of the particle.

f = y B₀

For hydrogen, y= 42.58 MHz / T.

Lamor with gradient vector:

f(r)=y(B₀+G•r)

where G is the gradient vector and r is the position vector.

The Larmor equation is important because it is the frequency at which the nucleus will absorb energy. The absorption of that energy will cause the proton to alter its alignment and ranges from 1-100 MHz in MRI. The equation states that the frequency of precession of the nuclear magnetic moment is directly proportional to the product of the magnetic field strength (B₀) and the gyromagnetic ratio (y).

Question 6

Explain when Resonance/Lamor’s frequency are applied

Answer 6

A particle can undergo a transition between the low and high energy states by the absorption of a photon. A particle in the lower energy state absorbs a photon and ends up in the upper energy state. The energy of this photon must exactly match the energy difference between the two states. The energy, E, of a photon is related to its frequency, f , by Planck’s constant (h = 6.626x10-34 J s).

E = fh

In NMR and MRI, the quantity f is called the resonance frequency and the Larmor frequency.

Question 7

Explain Precession

Answer 7

Precession is a wobbling motion that occurs when a spinning object is the subject of an external force.

Relevant to MRI, the proton of a hydrogen nucleus spins around its axis giving it an angular moment (quantum mechanics). Through the protons positive charge and its spin it generates a magnetic field and gets a magnetic dipole moment (MDM) parallel to the rotation axis. If placed in a magnetic field the magnetic dipole moment will precess about the direction of the magnetic field with an angular frequency (Larmor frequency). The Larmor equation dictates that the frequency of the precession at higher field strengths is higher.

Question 8

When does a photon gets absorbed by for instance a proton affected by an external a magnetic field?

Answer 8

When the energy of the photon matches the energy difference between the two spin states an absorption of energy occurs.

Question 9

In what frequency range does the frequencies of the photons for clinical MRI occur?

Answer 9

In the NMR experiment, the frequency of the photon is in the radio frequency (RF) range. In NMR spectroscopy, is between 60 and 800 MHz for hydrogen nuclei. In clinical MRI, is typically between 15 and 80 MHz for hydrogen imaging.

Question 10

What is the Magnetic flux density and the frequency of radio waves for a basic MRI setup?

Answer 10

• Magnetic flux density 1.5 T
• Linear magnetic field gradients
• Radio waves ca 63 MHz at 1.5 T (wavelength ca 0.5 m in tissue)

Question 11

Explain which tissues MRI versus CT is specifically good at detecting.

Answer 11

Structures with high density appear bright – CT is very good at depicting bone.

MRI provides very good soft tissue contrast.

Question 12

Describe the effects of external magnetic field and thermal energy.

Answer 12

Thermal energy
Chaos (at body temperature) The orientation of the spins of the ¹H nuclei are randomized, scrambled by molecular thermal motion

External magnetic field - Order
The magnetic field tends to line B0 up the magnetic moments of the ¹H nuclei.

Thermal equilibrium
The balance between chaos and order.

M
At 1T, the excess of magnetic moments of the ¹H nuclei aligned with the external magnetic field are 10 ppm. They produces a net magnetization, M.

Question 13

Explain the Motion of Magnetization

(Magnetization, Torque, Spin Angular Momentum, Precession, Relaxation)

Answer 13

Motion of the magnetization, M

Magnetization
The 1H nuclei in the human body, when placed in a magnetic field, B₀ , will build up a magnetization M

Torque
If M is brought out of the alignment with B₀ , it will experience a torque which acts to return M to alignment.

Spin Angular Momentum
The gyroscopic properties of the 1H nuclei prohibits M to simply flip back

Precession
and the torque results in a precession of M.

Relaxation
M will eventually relax and return to thermal equilibrium

Question 14

Explain Resonance.

Answer 14

Resonance

If impulses (or ”pushes”) are applied synchronous with the inherent motion of the system the resonance condition is fulfilled and energy is transferred to the system

Examples:

• The motion of the swing increases in amplitude
• M is brought into precession at increasing angles to B

Question 15

Explain the differences between Precession and Resonance (alternative view)

Answer 15

Nuclear precession is a long-term, spontaneous phenomenon, unaccompanied by energy exchange.

Nuclear resonance is a short-term, induced phenomenon, involving energy exchange between precessing spins and their environment.

Spins wobble (or precess) about the axis of the B_O field so as to describe a cone. This is called precession. Spinning protons are like dreidles spinning about their axis. Precession corresponds to the gyration of the rotating axis of a spinning body about an intersecting axis.

Resonance: exchange of energy at a specific frequency between the spins and the radio-frequency pulses

Question 16

Briefly explain T1 and T2 relaxation.

Answer 16

T1 relaxation
The build up of the magnetization towards thermal equilibrium Synonyms:
- spin-lattice relaxation
- longitudinal relaxation

T2 relaxation
The decay of induction (signal) towards zero.
Synonyms:
- spin-spin relaxation
- transversal relaxation

Question 17

Explain the Bloch Equations

Answer 17

Bloch Equations

In physics and chemistry, specifically in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and electron spin resonance (ESR), the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (Mx, My, Mz) as a function of time when relaxation times T1 and T2 are present.

Question 18

What does TE and TR stand for?

Answer 18

• TE: Time to echo (i.e. Time to signal recording)
• TR: Repetition time

Question 19

What is the difference between Gradient Echo and Spin Echo?

Answer 19

Gradient Echo and Spin Echo

• Spin Echo signal is generated by 2 RF-pulses
• Gradient Echo signal is generated by 1 RF-pulse + gradient reversal
• Spin Echo (but not Gradient Echo) compensates for field inhomogeneties.

Question 20

Which component of the nuclear magnetisation induces signal in the MR scanner?

Answer 20

MR Scanner

Only the transversal component of the nuclear magnetisation induces signal in the coil

Records the MR signal at echo time (TE)

 MR signal from tissue -> Greyscale in the image

Question 21

How does the conversion between longitudinal and transversal magnetization occurs?

Answer 21

Question 22

How does T1-weighted images of the brain appear?

Answer 22

T1-weighted (T1; short TR and short TE):

• Provides good contrast between gray matter (dark gray) and white matter (lighter gray) tissues, while CSF is void of signal (black).
• Water, such as CSF, as well as dense bone and air appear dark.
• Fat, such as lipids in the myelinated white matter, appears bright.
• Contrast between the neocortex and white matter is best.
• Contrast between some subcortical gray matter nuclei and white matter is fine but not as good as between cortex and white matter. These nuclei, such as the caudate and putamen, tend to have more white matter fibers and vascular infrastructure than other gray matter regions, increasing the brightness (i.e., lighter gray, more similar to white matter).
• Pathological processes, such as demyelination or inflammation, often increase water content in tissues, which decreases the signal on T1; white matter disease often shows up as darker areas in the lighter gray-colored white matter. (Extensive white matter disease on T1 (left); Moderate white matter disease on T1 (left)) Due to a better measure of water content, T2-weighted images are more sensitive to subtle white matter alterations.

Source: http://fmri.ucsd.edu/Howto/3T/structure.html

Question 23

How does T2-weighted images of the brain looks like?

Answer 23

T2-weighted (T2; long TR and long TE):

• Provides good contrast between CSF (bright) and brain tissue (dark). Some T2 sequences demonstrate additional contrast between gray matter (lighter gray) and white matter (darker gray).
• Water, such as CSF, appears bright, while air appears dark.
• Fat, such as lipids in the white matter, appears dark.
• Pathological processes, such as demyelination or inflammation, often increase water content in tissues, which increases signal on T2; white matter disease often shows up as brighter areas, (Extensive white matter disease on T2 (right); Moderate white matter disease on T2 (middle)) which makes subtle changes easier to detect.
• source: http://fmri.ucsd.edu/Howto/3T/structure.html

Question 24

How does PD-weighted images look like?

Answer 24

Proton density-weighted (PD; long TR and short TE):

• Provides good contrast between gray (bright) and white (darker gray) matter, with little contrast between brain and CSF.
• Water varies in signal, with CSF often gray while other fluids may be of higher signal intensity; air appears dark.
• Fat, such as lipids in the white matter, is relatively bright, although gray matter appears brighter than white matter.
• Subcortical nuclei and neocortex tend to be more similar in intensity than on T1.
• Pathological processes, such as demyelination or inflammation, often increase water content in tissues, which increases signal on PD; white matter disease often shows up as brighter areas but with signal different from CSF, unlike T2 (Moderate white matter disease on PD (right)) .
• Source: http://fmri.ucsd.edu/Howto/3T/structure.html

Question 25

Explain Magnetic susceptibility.

Answer 25

Magnetic susceptibility

• Ability of matter to become magnitized
• Physical property of matter
  
  • Typical volume susceptibility values
    
    • Air ~ 0 ppm
    • Soft tissue ~ -9 ppm

Question 26

Explain Bulk Magnetisation

Answer 26

Bulk magnetization of tissue

• Total magnetization of a tissue volume
• Proportional to the applied magnetic field
• The dominating component is diamagnetic (opposing the applied magnetic field)
• The nuclear magnetizations of various nuclei (paramagnetic, supporting the applied magnetic field) are very small

Question 27

Describe T2 vs T2* relaxation

Answer 27

T2 vs T2* relaxation

• T2:
  
  • Irreversible decrease of transversal magnetization due to processes at the molecular level.
• T*2:
  
  • Observed larger decrease of transversal magnetization
  • Additional dephasing contributes to T2*:
    
    • inhomogeneous magnetic field in the magnet
    • magnetic field inhomogeneities caused by susceptibility effects in the object

Question 28

Explain T1-relaxation time.

Answer 28

The T1 relaxation time, also known as the spin-lattice relaxation time, is a measure of how quickly the net magnetisation vector (NMV) recovers to its ground state in the direction of B0. The return of excited nuclei from the high energy state to the low energy or ground state is associated with loss of energy to the surrounding nuclei. Nuclear magnetic resonance was originally used to examine solids in the form of lattices, hence the name “spin-lattice” relaxation.

Question 29

Explain T2-relaxation time.

Answer 29

T2 relaxation times

T2 relaxation refers to the progressive dephasing of spinning dipoles following the 90° pulse as seen in a spin-echo sequence due to tissue-particular characteristics, primarily those that affect the rate of movement of protons, most of which are found in water molecules. This is alternatively known as spin-spin relaxation.

Immediately after the 90° pulse, all the spinning dipoles within the slice are exactly in phase. Almost immediately, they lose coherence as some spin slightly faster than the others. This dephasing effect has been likened to the opening of a chinese fan. The result is that the Mxycomponent of the magnetic vector decreases exponentially as a function of the T2 time constant.

Question 30

Explain T2* relaxation time.

Answer 30

T2* relaxation time

T2* decay refers to an exponential decrease in Mxy (i.e. signal strength) following the initial excitation pulse as a function of time constant T2*.

Following the excitation pulse, there is an immediate exponential loss of signal strength. This depends upon two factors:

static field non-uniformity within each voxel: due to imperfections in the construction of the scanner magnet itself, as well as from magnetic susceptibility effects in the patient inside the field

spin-spin interactions (T2 relaxation)

T2* decay is what actually a coil receiver detects immediately after termination of the induction pulse and is of much greater magnitude than T2 in tissues due to the inherent inhomogeneity of the magnetic field. If one had a “perfectly” uniform magnet and an object without susceptibility effects, the T2 and T2* would be equal.

The relationship between T2 and T2* can be illustrated by the multiecho spin echo sequence shown in Figure 2. The 180 degree RF pulses used to generate the echo are rephasing the spins that have undergone T2* decay. The gradual decline in signal from subsequent echos reflects T2 decay. T2* decay can be refocused by 180o pulses as in the simplified spin echo sequence in the figure but not be gradient refocusing seen in gradient echo sequences.

The effects of T2* can therefore be seen and utilized in gradient echo imaging and in the FID signal following a 90o RF pulse.

Question 31

How is the angle of magnetization accomplished?

Answer 31

The angle the magnetization is flipped is determined by the duration and strength of the RF pulse. Pulses are characterized by their flip angles.

Pulses with 90° and 180° flip angles are the most common but smaller flip angle pulses are also used in some imaging methods, such as gradient echo imaging.

Question 32

Explain longitudinal magnetisation and relaxation time

Answer 32

Longitudinal magnetisation Relaxation times

As we have seen, when tissue is placed in a magnetic field, it becomes magnetized in the longitudinal direction. It will remain in this state until the magnetic field is changed or until the magnetization is redirected by the application of an RF pulse. If the magnetization is temporarily redirected by an RF pulse, it will then, over a period of time, return to its original longitudinal position. If we consider only the longitudinal magnetization, it regrows after it has been reduced to zero, or saturated. This regrowth, or recovery, of longitudinal magnetization is the relaxation process, which occurs after saturation. The time required for the longitudinal magnetization to regrow, or relax, depends on characteristics of the material and the strength of the magnetic field.

Longitudinal magnetization does not grow at a constant rate, but at an exponential rate. An important concept to remember is that the MR image is an image of magnetized tissue with brightness indicating the level of magnetization. During the relaxation process, the level of magnetization is changing. Therefore, the brightness of tissue (if we could see it) is also changing as indicated by the scale on the right of the illustration. Saturation turns the tissue dark and then it recovers brightness during the relaxation period.

T1 contrast

The time required for a specific level of longitudinal magnetization regrowth varies from tissue to tissue. In this illustration we watch the intensity of brightness of a voxel of tissue during the relaxation process. Let us recall that the brightness of a tissue (RF signal intensity) is determined by the level of magnetization existing in a voxel of tissue at any instant in time. What we see in an image depends on when we “snap the picture” during the relaxation process. The important thing to notice is that the tissue with the shortest T1 has the highest level of magnetization at any particular time. The clinical significance of this is that tissues with short T1 values will be bright in T1-weighted images.

Question 33

Explain Transverse magnetization and relaxation

.

Answer 33

Transverse magnetization and relaxation

Transverse magnetization is produced by applying a pulse of RF energy to the magnetized tissue. This is typically done with a 90˚ pulse, which converts longitudinal magnetization into transverse magnetization. Transverse magnetization is an unstable, or excited, condition and quickly decays after the termination of the excitation pulse. The decay of transverse magnetization is also a relaxation process, which can be characterized by specific relaxation times, or T2 values. Different types of tissue have different T2 values that can be used to discriminate among tissues and contribute to image contrast.

Transverse magnetization is used during the image formation process for two reasons: (1) to develop image contrast based on differences in T2 values; and (2) to generate the RF signals emitted by the tissue. Longitudinal magnetization is an RF silent condition and does not produce any signal. However, transverse magnetization is a spinning magnetic condition within each tissue voxel, and that generates an RF signal. As we will see in the next chapter, each imaging cycle must conclude with transverse magnetization to produce the RF signal used to form the image.

The characteristics of transverse magnetization and relaxation are quite different from those for the longitudinal direction. A major difference is that transverse magnetization is an unstable condition and the relaxation process results in the decay, or decrease, in magnetization. The T2 value is the time required for 63% of the initial magnetization to dissipate. After one T2, 37% of the initial magnetization is present.

T2 Contrast

The difference in T2 values of tissues is the source of contrast in T2-weighted images. This is illustrated in Figure 4-8. Here we watch two tissues, with different T2 values, during the relaxation process. We see that they are both getting darker with time as the magnetization decays. However, they are not getting darker at the same rate. The tissue with the shorter T2 becomes darker faster leaving the tissue with the longer T2 to be bright at times during the relaxation time.

T2* Magnetic field effects

A second effect, which produces relatively rapid dephasing of the nuclei and loss of transverse magnetization, is the inherent inhomogeneity of the magnetic field within each individual voxel. The field inhomogeneities are sufficient to produce rapid dephasing. This effect, which is different from the basic T2 characteristics of the tissue, tends to mask the true relaxation characteristics of the tissue. In other words, the actual transverse magnetization relaxes much faster than the tissue characteristics would indicate. This real relaxation time is designated as T2*. The value of T2* is usually much less than the tissue T2 value, as illustrated in Figure 4-11. Several factors can contribute to field inhomogeneities and to T2* decay. One is the general condition of the magnetic field. Some fields are more homogeneous than others. Another factor is that different tissues or materials in the body might have different magnetic susceptibilities. Susceptibility is a characteristic of a material that determines its ability to become magnetized when it is in a magnetic field. If a region of tissue contains materials with different susceptibilities, this results in a reduction of field homogeneity.

Question 34

Explain Proton Density

Answer 34

Proton Density

An image produced by controlling the selection of scan parameters to minimize the effects of T1 and T2, resulting in an image dependent primarily on the density of protons in the imaging volume. Proton density contrast is a quantitative summary of the number of protons per unit tissue. The higher the number of protons in a given unit of tissue, the greater the transverse component of magnetization, and the brighter the signal on the proton density contrast image. Conversely the lower the number of protons in a given unit of tissue, the less the transverse magnetization and the darker the signal on the proton density image. Also called (Rho) r-weighted.

Question 35

Explain the Radio frequency signal path into the MR system

Answer 35

Radio frequency signal path into the MR system

Question 36

Visualisation of MRI Pulse Sequence

Answer 36

MRI Pulse Sequence

Question 37

Explain k-space

Answer 37

k-space

The data matrix: a sampled version of the central part of the object in k-space.

Each point in k-space correspond to a spatial harmonic in the metric space.

Reciprocal space and Fourier space are synonyms for k-space.

Question 38

Explain the translation between pulse sequence diagram and k-space trajectory

Answer 38

Translation between pulse sequence diagram and k-space trajectory

A few rules for the excursions in k-space

• The excitation pulse starts the trajectory
• The trajectory starts in origo in k-space
• The end point of the trajectory moves with speed and direction given by the gradient strength and direction
• A 180°-pulse causes the end point of the trajectory to be point mirrored in origo
• The signal decreases with time due to T2 relaxation

Question 39

Analog for MRI

Answer 39

MRI - a radio station with a big magnet

Question 40

What are the hardware components of MRI?

Answer 40

Hardware Components MRI

1. Big magnet
2. Dewars* and cryogenic** equipment
3. Transmit and receiver coils
4. Transmit and receiver amplifiers
5. Magnetic field gradient coils
6. Computer(s)
7. Ancillary equipment, physiological monitoring, safety sensors (SAR, temperature, O₂)

*A large vacuum jacketed double walled container generally made out of stainless steel that is used to transport cryogens.

** A cooling agent, typically liquid helium or liquid nitrogen used to reduce the temperature of the magnet windings in a superconducting magnet.

Question 41

Explain different types of cardiac gating methods

Answer 41

Cardiac Gating Methods

• ECG Leads
  
  • Early detection of systole
  • Potential hazard of skin burns
  • ECG distorted and not of diagnostic value
• Peripheral gating
  
  • Easy setup with photo sensors place on finger tip
  • Delayed detection of systole
• MR scan with pencil excitation
  
  • Technically more difficult to implement
  • Requires real time processing of 1D MR Data

Question 42

Complex MR signal - Which form is usually displayed?

Answer 42

Complex MR Signal

• Most diagnostic MR images are magnitude images.
• Phase can be used to encode information, e.g. motion

Question 43

What is VENC?

Answer 43

VENC

VENC = Velocity to encode 180 degrees phase shift

Question 44

Explain Magnetisation phase vs Magnetisation dephase

Answer 44

Magnetisation phase vs Magnetisation dephasing

• Magnetisation phase: In a homogeneous magnetic field, the magnetisation vectors within a small volume might precess in the m_xy plane indefinitely in phase
• Magnetisation dephasing: However, over time, due to small variations in the magnetic field, which cause the magnetisation vectors to precess at slightly different frequencies, the vectors will begin to get out of phase with each other.
• In phase: Yields maximum signal. Image appear bright.
• Phase incoherence: Signal loss. Image pixels appear less bright and dark.

Question 45

Explain SWI

Answer 45

Susceptibility Weighted Images (SWI)

• SWI uses a gradient echo scan (T2*-weighted)
• The phase image is high-pass (HP) filtered to remove unwanted artifacts.
• The magnitude image is then combined with the phase image to create an enhanced contrast magnitude image referred to as SWI.

Question 46

Give examples of MR Spectroscopy

Answer 46

MR Spectroscopy

• Singel voxel techniques using three intersecting slices to locate a single voxel from which the spectrum is measured.
  
  • STEAM - STimulated Echo Acquistion Mode
  • PRESS - Point REsolved Spectroscopy Spin Echo
  • MRSI - Magnetic Resonance Spectroscopic Imaging

Question 47

Explain the Larmor Equation in prose.

Answer 47

Larmor Equation (as explained on exam solution)

f = y*B0

• B₀ = Strenght of Magnetic Field [Tesla]
• y* (\gamma) = gyromagnetic ratio (\y/(2*\pi). [Hz/T]
  For hydrogen 42.58 MHz / T.
• f = larmor frequency [Hz] (if using above stated units).
• It expresses that frequency at which net magnitisation precesses (spin) around B₀ axis is directly proportional to B0.
• Note: Microscopic spins add up to form net magnetisation which is aligned along B₀ axis. When RF pulse tips this net magnetisation out of alignment it starts to precess at larmor frequency around B₀ axis.

Question 48

The magnetization of hydrogen nuclei provide the source of signal for clinical MRI and the pulse sequence defines the scanning scheme. The two different relaxation processes for the nuclear magnetization are a main contribution to MR contrast.

a) Which relaxation process provided the contrast when cerebro-spinal fluid in the ventricles in the brain appears darker than brain tissues (white matter and grey matter) in MR image contrast.
b) Which component of the nuclear magnetization does the relaxation process in a) apply to.
c) Give the two pulse sequence timing parameters that affect the basic MR contrast (symbol, name and unit)
d) State (qualitively) how these parameters should be chosen to produce the image contrast in (a). Motivate this choice.

Answer 48

(According to Solution on Exam)

a) T1, because T1 is exponentially growing longitudinal magnetization and CSF has the longest T1.
b) It applies to longitudinal magnetization.
c) TR = Repition time [units ms], TE= Time to Echo [units ms]
d) For T1 relaxation, we need short TE and TR.

• Short TR because if we keep TR long enough the longitudinal magnetization is fully recovered and then we cannot distinguish between different tissues as all these tissues will eventually have the same longitudinal magnetization.
• Short TE because if TE is long it will be T2 weighted and if TE is very short or 0 it will be PD weighted, therefore we need to make TE short, but not too short.

Question 49

Explain Boltzmann distribution

Answer 49

These are governed by thermal equilibrium condition, which are characterized by the Boltzmann distribution. Letting N+ be the higher energy state (spin-down) and N- be the lower energy state, Boltzmann dictates that:

N+/N-=e^{-\delta E/kt}

Where k=Boltzmann’s constant (8.62e-5 eV/K or 1.38e-23 J/K)

T = temperature (human body temperature = 310 K) ΔE = hγ B0

Important! Please note that ΔN, then number of excess nuclei in lower vs. upper energy states is proportional to B0. It is also proportional to γ. These excess nuclei are the source of magnetization for all MRI experiments. It follows then, that a larger magnetic field, B0, will generate larger magnetization to perform our imaging experiments and different nuclei will develop differing amounts of magnetization depending on their concentration in the body (NT) and their γ.

Question 50

Answer 50

As B0 increases, so does the energy gap between the 2 quantom spin states. This is contained in the \delta E term. K = Boltzmanns constant, T= temperature in Kelvin. Solving this equation yields the spin-up vs spin-down ratio for H (hydrogen has only 2 spin states). In thermal equilibrium, room temperature, there’s a small inversion in the ratio as B0 keeps a certain amount of H atoms in the higher energy spin state.

Question 51

Explain RF excitation: When is it used and what for? What kind of signal (frequency, shape/envelope, polarization, phase) are usually used for RF excitation?